This series of files compile all analyses done during Chapter 3:
- Section 1 presents the calculation of the indices of exposure.
- Section 2 presents variable exploration and regressions results.
- Section 3 presents species distribution models.
All analyses have been done with R 4.0.4.
Click on the table of contents in the left margin to assess a specific analysis.
Click on a figure to zoom it
⏪ | 🏠 | 📄 | ⏩
Sources of activity considered for the analyses:
- aquaculture: mussel farm (AquaInf)
- city: general diffusive influence, wharves (CityInf, CityWha)
- industry: general diffusive influence, wharves (Indu, InduWha)
- sediment dredging: collection zones, dumping zones (DredColl, DredDump)
- commercial shipping: mooring sites, traffic routes (ShipMoor, ShipTraf)
- sewers: rainwater drains, wastewater drains (SewRain, SewWast)
Fisheries data considered for the analyses (expressed as number of fishing events or kilograms of collected individuals for each gear):
| Dredge |
FishDred |
2010-2014 |
21 |
Mactromeris polynyma |
| Net |
FishNet |
2010 |
5 |
Clupea harengus, Gadus morhua |
| Trap |
FishTrap |
2010-2015 |
1061 |
Buccinum sp., Cancer irroratus, Chionoecetes opilio, Homarus americanus |
| Bottom-trawl |
FishTraw |
2013-2014 |
2 |
Pandalus borealis |
1. Spatial variation of exposure indices
Here, we compute semivariograms for each exposure index (on the whole raster, not only extracted values at the stations).
Aquaculture
## Model selected: Lin
## nugget = 0; sill = 0.00389; range = 2.29619; kappa = 0.5

City
## Model selected: Lin
## nugget = 0.00025; sill = 0.00602; range = 8.57222; kappa = 0.5

Sediment dredging
## Model selected: Exp
## nugget = 0.00021; sill = 0.02042; range = 4.52941; kappa = 0.5

Industry
## Model selected: Sph
## nugget = 1e-04; sill = 0.0072; range = 10.10924; kappa = 0.5

Sewers
## Model selected: Exp
## nugget = 0; sill = 0.03366; range = 43.15003; kappa = 0.5

Shipping
## Model selected: Lin
## nugget = 0; sill = 0.06455; range = 4.27615; kappa = 0.5

Fisheries
## Model selected: Lin
## nugget = 0; sill = 0.02483; range = 3.40343; kappa = 0.5

2. Relationships with abiotic parameters
2.1. Covariation
Several types of models were considered to explore relationships: linear, quadratic, exponential and logarithmic. The model with the highest \(R^{2}\) is presented on each plot.
⚠️ Only linear models were implemented for now, as there are some bugs with the calculation of the others.
Aquaculture

City

Sediment dredging

Industry

Sewers

Shipping

Fisheries

Cumulative exposure

2.2. Correlation
Correlations have been calculated with Spearman’s rank coefficient.
Correlation coefficients between exposure indices and ecosystem variables
| aquaculture |
-0.438 |
0.164 |
0.475 |
-0.435 |
-0.055 |
-0.693 |
-0.785 |
-0.741 |
-0.673 |
-0.627 |
-0.78 |
-0.76 |
-0.725 |
-0.737 |
0.315 |
0.002 |
-0.021 |
0.347 |
0.19 |
| city |
-0.155 |
-0.067 |
0.427 |
-0.273 |
-0.096 |
-0.246 |
-0.163 |
-0.171 |
0.086 |
-0.004 |
-0.154 |
-0.243 |
-0.167 |
-0.015 |
-0.108 |
-0.036 |
-0.153 |
-0.055 |
0.035 |
| dredging |
0.275 |
-0.084 |
-0.091 |
0.103 |
0.055 |
0.264 |
0.19 |
0.407 |
0.574 |
0.649 |
0.55 |
0.219 |
0.324 |
0.482 |
-0.215 |
-0.133 |
0.049 |
-0.13 |
-0.023 |
| industry |
0.159 |
-0.071 |
-0.016 |
0.045 |
0.069 |
0.176 |
0.115 |
0.348 |
0.514 |
0.588 |
0.504 |
0.157 |
0.253 |
0.405 |
-0.246 |
-0.115 |
0.053 |
-0.198 |
-0.076 |
| sewers |
0.254 |
-0.037 |
-0.313 |
0.268 |
0.249 |
0.609 |
0.581 |
0.654 |
0.694 |
0.591 |
0.707 |
0.579 |
0.689 |
0.689 |
-0.353 |
-0.063 |
0.021 |
-0.369 |
-0.174 |
| shipping |
0.456 |
-0.249 |
-0.291 |
0.314 |
-0.015 |
0.537 |
0.504 |
0.618 |
0.693 |
0.677 |
0.708 |
0.549 |
0.576 |
0.687 |
-0.19 |
-0.06 |
0.022 |
-0.172 |
-0.095 |
| fisheries |
-0.492 |
0.202 |
0.376 |
-0.378 |
-0.138 |
-0.567 |
-0.541 |
-0.552 |
-0.606 |
-0.576 |
-0.585 |
-0.54 |
-0.563 |
-0.613 |
0.309 |
0.173 |
-0.066 |
0.224 |
-0.015 |
| cumulative_exposure |
0.282 |
-0.114 |
-0.163 |
0.198 |
0.085 |
0.364 |
0.264 |
0.407 |
0.552 |
0.57 |
0.525 |
0.315 |
0.41 |
0.505 |
-0.108 |
-0.047 |
0.001 |
-0.125 |
-0.123 |
p-values of correlation test between exposure indices and ecosystem variables
| aquaculture |
2.182e-06 |
0.08972 |
2.088e-07 |
2.619e-06 |
0.574 |
9.031e-17 |
9.296e-24 |
5.052e-20 |
1.466e-15 |
3.917e-13 |
2.796e-23 |
1.567e-21 |
7.356e-19 |
9.114e-20 |
0.0009079 |
0.9815 |
0.8288 |
0.0002382 |
0.04944 |
| city |
0.1087 |
0.4921 |
3.982e-06 |
0.004225 |
0.3206 |
0.01043 |
0.09275 |
0.07674 |
0.3781 |
0.964 |
0.1118 |
0.01126 |
0.08362 |
0.8744 |
0.2674 |
0.7138 |
0.1134 |
0.5708 |
0.7171 |
| dredging |
0.004038 |
0.3876 |
0.3492 |
0.2869 |
0.574 |
0.005687 |
0.04861 |
1.217e-05 |
8.309e-11 |
2.962e-14 |
6.813e-10 |
0.02309 |
0.000633 |
1.283e-07 |
0.02517 |
0.171 |
0.6121 |
0.1789 |
0.8096 |
| industry |
0.1007 |
0.465 |
0.8689 |
0.6459 |
0.4811 |
0.06919 |
0.2347 |
0.0002275 |
1.3e-08 |
2.144e-11 |
2.783e-08 |
0.1043 |
0.008203 |
1.389e-05 |
0.01022 |
0.236 |
0.5892 |
0.03971 |
0.4341 |
| sewers |
0.007974 |
0.702 |
0.000962 |
0.004998 |
0.009281 |
2.623e-12 |
4.439e-11 |
1.762e-14 |
8.768e-17 |
1.703e-11 |
1.192e-17 |
5.084e-11 |
1.659e-16 |
1.805e-16 |
0.000176 |
0.5189 |
0.8284 |
8.325e-05 |
0.07195 |
| shipping |
7.165e-07 |
0.009324 |
0.002213 |
0.0009345 |
0.8743 |
2.146e-09 |
2.655e-08 |
1.041e-12 |
1.003e-16 |
9.205e-16 |
1.105e-17 |
7.68e-10 |
7.258e-11 |
2.359e-16 |
0.04853 |
0.5351 |
0.8202 |
0.07554 |
0.3296 |
| fisheries |
6.275e-08 |
0.03585 |
6.17e-05 |
5.585e-05 |
0.1551 |
1.607e-10 |
1.476e-09 |
6.146e-10 |
3.727e-12 |
6.679e-11 |
2.989e-11 |
1.623e-09 |
2.366e-10 |
1.852e-12 |
0.001128 |
0.07296 |
0.496 |
0.01998 |
0.8735 |
| cumulative_exposure |
0.003134 |
0.2417 |
0.0927 |
0.04022 |
0.3831 |
0.0001071 |
0.005753 |
1.227e-05 |
5.814e-10 |
1.193e-10 |
5.558e-09 |
0.0008975 |
1.026e-05 |
2.504e-08 |
0.2678 |
0.6258 |
0.9893 |
0.1967 |
0.2062 |

3. Relationships with benthic communities
3.1. Taxa identity
The most abundant taxa in our study area are:
- Density: B.neotena (1969), E. integra (1158), P.grandimana (1092), Nematoda (1044) and M. calcarea (575)
- Biomass: E. parma (biomass of 531.5), Strongylocentrotus sp. (65.3), N. incisa (58.5), M. calcarea (45.4) and S. groenlandicus (34.3)
The following graphs present the distribution of sampled phyla along index of cumulative exposure, according to density (left panel) or biomass (right).
Exposure categories are based on the exposure index: the higher the index, the lower the status. Maximum cumulative exposure is 1.955, and the five categories are from ‘bad’ to ‘high’, with 20 %, 40 %, 60 % or 80 % of the maximum exposure.
4. Regressions
4.1. Data manipulation
For the following analyses, independant variables are exposure indices, dependant variables are community characteristics. Variables have been standardized by mean and standard-deviation.
All stations and predictors were selected for the regressions, as we are interested in each of them (following graphs are for information only).

Correlation coefficients between exposure indices
| aquaculture |
1 |
0.061 |
-0.364 |
-0.308 |
-0.672 |
-0.7 |
0.72 |
| city |
0.061 |
1 |
0.334 |
0.325 |
0.131 |
0.22 |
-0.201 |
| dredging |
-0.364 |
0.334 |
1 |
0.961 |
0.668 |
0.686 |
-0.469 |
| industry |
-0.308 |
0.325 |
0.961 |
1 |
0.691 |
0.598 |
-0.365 |
| sewers |
-0.672 |
0.131 |
0.668 |
0.691 |
1 |
0.65 |
-0.581 |
| shipping |
-0.7 |
0.22 |
0.686 |
0.598 |
0.65 |
1 |
-0.72 |
| fisheries |
0.72 |
-0.201 |
-0.469 |
-0.365 |
-0.581 |
-0.72 |
1 |

4.2. Univariate regressions
We used linear models for the regressions on community characteristics. Variables have been standardized by mean and standard-deviation (coefficients need to be back-transformed to be used in predictive models). Variable selection was not needed here, as we are interested in all exposure indices.
Results of regressions (coefficients with a significant p-value for marginal tests) are shown on the table below:
| Depth |
+ |
|
|
+ |
+ |
| Aquaculture |
|
|
|
|
|
| City |
|
|
|
|
|
| Dredging |
|
|
|
|
|
| Industry |
|
|
|
|
|
| Sewers |
|
|
- |
|
|
| Shipping |
|
|
|
|
|
| Fisheries |
|
|
|
|
|
| Adjusted \(R^{2}\) |
0.2 |
0.02 |
0.02 |
0.3 |
0.15 |
Details of the regressions, with diagnostics and cross-validation, are summarized below.
Richness
## FULL MODEL
## Adjusted R2 is: 0.2
Fitting linear model: S ~ depth + aquaculture + city + dredging + industry + sewers + shipping + fisheries
| (Intercept) |
-2.755e-16 |
0.08611 |
-3.2e-15 |
1 |
|
| depth |
0.2244 |
0.1005 |
2.232 |
0.02785 |
* |
| aquaculture |
0.1323 |
0.09663 |
1.369 |
0.174 |
|
| city |
0.0227 |
0.09686 |
0.2344 |
0.8152 |
|
| dredging |
-0.03145 |
0.1112 |
-0.2828 |
0.7779 |
|
| industry |
-0.1425 |
0.1338 |
-1.065 |
0.2895 |
|
| sewers |
-0.1207 |
0.1376 |
-0.8777 |
0.3823 |
|
| shipping |
0.1112 |
0.09715 |
1.145 |
0.255 |
|
| fisheries |
0.1734 |
0.09747 |
1.779 |
0.07831 |
|
## RMSE from cross-validation: 0.9206012
Variance Inflation Factors
| VIF |
1.16 |
1.12 |
1.12 |
1.29 |
1.55 |
1.59 |
1.12 |
1.13 |

Density
## FULL MODEL
## Adjusted R2 is: 0.02
Fitting linear model: N ~ depth + aquaculture + city + dredging + industry + sewers + shipping + fisheries
| (Intercept) |
1.866e-16 |
0.09512 |
1.961e-15 |
1 |
|
| depth |
-0.2039 |
0.111 |
-1.837 |
0.06923 |
|
| aquaculture |
-0.001951 |
0.1067 |
-0.01828 |
0.9855 |
|
| city |
0.07397 |
0.107 |
0.6913 |
0.491 |
|
| dredging |
-0.08934 |
0.1228 |
-0.7273 |
0.4687 |
|
| industry |
-0.1808 |
0.1478 |
-1.223 |
0.2242 |
|
| sewers |
0.1457 |
0.152 |
0.9588 |
0.34 |
|
| shipping |
-0.07382 |
0.1073 |
-0.6879 |
0.4931 |
|
| fisheries |
0.08586 |
0.1077 |
0.7975 |
0.4271 |
|
## RMSE from cross-validation: 1.045544
Variance Inflation Factors
| VIF |
1.16 |
1.12 |
1.12 |
1.29 |
1.55 |
1.59 |
1.12 |
1.13 |

Biomass
## FULL MODEL
## Adjusted R2 is: 0.02
Fitting linear model: B ~ depth + aquaculture + city + dredging + industry + sewers + shipping + fisheries
| (Intercept) |
-1.226e-16 |
0.09534 |
-1.286e-15 |
1 |
|
| depth |
-0.1858 |
0.1113 |
-1.67 |
0.09812 |
|
| aquaculture |
-0.1569 |
0.107 |
-1.467 |
0.1456 |
|
| city |
-0.1966 |
0.1072 |
-1.833 |
0.06984 |
|
| dredging |
0.008365 |
0.1231 |
0.06794 |
0.946 |
|
| industry |
0.1966 |
0.1482 |
1.327 |
0.1875 |
|
| sewers |
-0.3756 |
0.1523 |
-2.466 |
0.01539 |
* |
| shipping |
-0.08828 |
0.1076 |
-0.8207 |
0.4138 |
|
| fisheries |
-0.02274 |
0.1079 |
-0.2107 |
0.8335 |
|
## RMSE from cross-validation: 1.007
Variance Inflation Factors
| VIF |
1.16 |
1.12 |
1.12 |
1.29 |
1.55 |
1.59 |
1.12 |
1.13 |

Diversity
## FULL MODEL
## Adjusted R2 is: 0.3
Fitting linear model: H ~ depth + aquaculture + city + dredging + industry + sewers + shipping + fisheries
| (Intercept) |
3.142e-16 |
0.08045 |
3.906e-15 |
1 |
|
| depth |
0.4944 |
0.09391 |
5.265 |
8.175e-07 |
* * * |
| aquaculture |
0.1016 |
0.09028 |
1.126 |
0.263 |
|
| city |
0.08284 |
0.0905 |
0.9154 |
0.3622 |
|
| dredging |
0.1236 |
0.1039 |
1.189 |
0.2372 |
|
| industry |
-0.1761 |
0.125 |
-1.409 |
0.1621 |
|
| sewers |
-0.095 |
0.1285 |
-0.7391 |
0.4616 |
|
| shipping |
0.02914 |
0.09077 |
0.321 |
0.7489 |
|
| fisheries |
-0.03719 |
0.09107 |
-0.4084 |
0.6839 |
|
## RMSE from cross-validation: 0.912593
Variance Inflation Factors
| VIF |
1.16 |
1.12 |
1.12 |
1.29 |
1.55 |
1.59 |
1.12 |
1.13 |

Evenness
## FULL MODEL
## Adjusted R2 is: 0.15
Fitting linear model: J ~ depth + aquaculture + city + dredging + industry + sewers + shipping + fisheries
| (Intercept) |
1.392e-17 |
0.08846 |
1.573e-16 |
1 |
|
| depth |
0.4276 |
0.1032 |
4.141 |
7.277e-05 |
* * * |
| aquaculture |
0.01141 |
0.09926 |
0.115 |
0.9087 |
|
| city |
0.09542 |
0.0995 |
0.959 |
0.3399 |
|
| dredging |
0.1729 |
0.1142 |
1.514 |
0.1333 |
|
| industry |
-0.1712 |
0.1375 |
-1.246 |
0.2159 |
|
| sewers |
-0.02464 |
0.1413 |
-0.1744 |
0.8619 |
|
| shipping |
-0.07699 |
0.0998 |
-0.7715 |
0.4423 |
|
| fisheries |
-0.1746 |
0.1001 |
-1.744 |
0.08432 |
|
## RMSE from cross-validation: 1.066839
Variance Inflation Factors
| VIF |
1.16 |
1.12 |
1.12 |
1.29 |
1.55 |
1.59 |
1.12 |
1.13 |

Annelida density
## FULL MODEL
## McFadden's pseudo-R2 is: 0.14
Fitting generalized (poisson/log) linear model: annelids ~ depth + aquaculture + city + dredging + industry + sewers + shipping + fisheries
| (Intercept) |
3.314 |
0.01923 |
172.4 |
0 |
* * * |
| depth |
-0.3534 |
0.02507 |
-14.1 |
4.064e-45 |
* * * |
| aquaculture |
0.117 |
0.01655 |
7.067 |
1.58e-12 |
* * * |
| city |
0.09321 |
0.01825 |
5.108 |
3.248e-07 |
* * * |
| dredging |
-0.1001 |
0.02901 |
-3.448 |
0.0005642 |
* * * |
| industry |
-0.1914 |
0.03421 |
-5.595 |
2.203e-08 |
* * * |
| sewers |
-0.004193 |
0.03273 |
-0.1281 |
0.8981 |
|
| shipping |
0.1182 |
0.01862 |
6.348 |
2.177e-10 |
* * * |
| fisheries |
-0.07557 |
0.02359 |
-3.204 |
0.001354 |
* * |
## Unbiased RMSE from cross-validation: 35.86371
Variance Inflation Factors
| VIF |
1.24 |
1.16 |
1.14 |
1.32 |
1.56 |
1.63 |
1.15 |
1.13 |

Arthropoda density
## FULL MODEL
## McFadden's pseudo-R2 is: 0.18
Fitting generalized (poisson/log) linear model: arthropods ~ depth + aquaculture + city + dredging + industry + sewers + shipping + fisheries
| (Intercept) |
3.614 |
0.01706 |
211.8 |
0 |
* * * |
| depth |
-0.08957 |
0.01865 |
-4.802 |
1.568e-06 |
* * * |
| aquaculture |
-0.08194 |
0.02247 |
-3.646 |
0.0002666 |
* * * |
| city |
0.1337 |
0.01535 |
8.708 |
3.081e-18 |
* * * |
| dredging |
-0.1031 |
0.02307 |
-4.468 |
7.88e-06 |
* * * |
| industry |
-0.696 |
0.03437 |
-20.25 |
3.528e-91 |
* * * |
| sewers |
0.7409 |
0.0275 |
26.94 |
7.506e-160 |
* * * |
| shipping |
-0.07169 |
0.01609 |
-4.455 |
8.371e-06 |
* * * |
| fisheries |
0.07277 |
0.01654 |
4.4 |
1.085e-05 |
* * * |
## Unbiased RMSE from cross-validation: 89.93936
Variance Inflation Factors
| VIF |
1.26 |
1.1 |
1.11 |
1.23 |
1.98 |
2.08 |
1.11 |
1.13 |

Mollusca density
## FULL MODEL
## McFadden's pseudo-R2 is: 0.18
Fitting generalized (poisson/log) linear model: molluscs ~ depth + aquaculture + city + dredging + industry + sewers + shipping + fisheries
| (Intercept) |
2.468 |
0.03023 |
81.64 |
0 |
* * * |
| depth |
0.036 |
0.03013 |
1.195 |
0.2321 |
|
| aquaculture |
0.0685 |
0.02369 |
2.892 |
0.00383 |
* * |
| city |
0.2253 |
0.02329 |
9.673 |
3.913e-22 |
* * * |
| dredging |
-0.08718 |
0.04091 |
-2.131 |
0.03308 |
* |
| industry |
0.2496 |
0.0353 |
7.073 |
1.52e-12 |
* * * |
| sewers |
-0.3279 |
0.04496 |
-7.293 |
3.033e-13 |
* * * |
| shipping |
-0.2978 |
0.04308 |
-6.913 |
4.747e-12 |
* * * |
| fisheries |
0.07146 |
0.02425 |
2.946 |
0.003215 |
* * |
## Unbiased RMSE from cross-validation: 20.60514
Variance Inflation Factors
| VIF |
1.2 |
1.14 |
1.2 |
1.5 |
1.51 |
1.43 |
1.19 |
1.1 |

4.3. Multivariate regression
The model selected by the DistLM procedure has a \(R^{2}\) of 0.22. Colours represent the value of the cumulative exposure index (the bluer, the higher).


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